Preheat oven to 450°F. Coat a 1 1/2-quart baking dish with cooking spray.
In a medium bowl, combine the squash, 2 tablespoons Parmesan, salt, rosemary, and pepper. Spoon the mixture into the prepared dish. Sprinkle with the remaining 2 tablespoons of Parmesan and the shredded Asiago cheese too.
Bake for 20 minutes.
ROASTING YOUR BUTTERNUT SQUASH: Preheat your oven to 400 degrees F. Cut your butternut squash in half, scrape out the seeds and discard. Place them cut-side-up on a lined baking sheet. Drizzle with a little olive oil, and sprinkle with salt and pepper. Roast in the preheated oven until squash is fork- tender and lightly browned, 50 to 60 minutes. Let cool, scoop out the pulp, and then mash it up for your recipe!
TIP: If you roast your butternut squash ahead of time, you can refrigerate it until ready to use. Bring it to room temperature again before using in this recipe.